# NCERT Class 12-Mathematics: Exemplar Chapter – 4 Determinants Part 11 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 22**:

Prove that is divisible by and find the quotient

**Answer**:

Let

Now, expanding along

Hence, given determinant is divisible by and quotient is

**Question 23**:

If , prove that

**Answer**:

Given:

Taking LHS,

Expanding along the first row, we get

It is given that

Hence Proved

## Objective Type Questions (M. C. Q.)

### Choose the Correct Answer from Given Four Options in Each of the Exercises from 24 to 37

**Question 24**:

If , then value of is

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 25**:

The value of determinant

(A)

(B)

(C)

(D) None of these

**Answer: (C)**

**Question 26**:

The area of a triangle with vertices and is . units. The value of will be

(A)

(B)

(C)

(D)

**Answer: (B)**